I think overall mass would definitely play a factor in determining the maximum speeds of a starship, although I'm not certain that overall tonnage would play a part. I say that because Warp Speed isn't dependant on internal factors such as the crew or the cargo, it's more about the mass of the ship, the gravitational conditions and the stability of the projected warp field.
In Trek, the ships always drop out of warp when they enter various anomalous areas of space. This is usually followed by a line such as "We've hit a gravimetric distortion", etc. We can assume from that, that FTL speeds cannot be attained whilst within big scale gravitational variances. This might also be applied to a planetary level, more specifically the level of gravity on a planet. It might be impossible for all we know for a ship to create a warp field whilst inside the gravity field of certain planets.